An iterative method for nonlinear semidefinite programming with the distance information to a cone boundary

• Project/Area Number: 24710161
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Social systems engineering/Safety system
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: YAMASHITA Makoto 東京工業大学, 情報理工学(系)研究科, 准教授 (20386824)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 数理最適化 / 非線形最適化 / 半正定値計画問題 / 数値計算 / 応用数学

Outline of Final Research Achievements

Nonlinear semidefinite programs are optimization problems with a constraint on the eigenvalues of a variable matrix, and the range of applications includes optimization with uncertainty and financial engineering.
We propose an iterative method for box-constrained nonlinear semidefinite programs using the distance information from the current point to the boundary of a positive semidefinite cone.
We verified through numerical tests that the proposed method is more effective for box-constrained problems that have strongly nonlinear functions than a feasible direction method.

Research Products

• [Journal Article] Fast implementation for semidefinite programs with positive matrix completion (2015)
  • Author(s): Makoto Yamashita and Kazuhide Nakata
  • Journal Title: Optimization Methods and Software Volume: 30 Issue: 5 Pages: 1030-1049
  • DOI: 10.1080/10556788.2015.1014554
  • Peer Reviewed / Open Access
• [Journal Article] Using semi-definite programming to optimize unequal deployment of genotypes to a clonal seed orchard (2014)
  • Author(s): Jon Ahlinder, Tim. J. Mullin, Makoto Yamashita
  • Journal Title: Tree Genetics & Genomes Volume: 10(1) Issue: 1 Pages: 27-34
  • DOI: 10.1007/s11295-013-0659-z
  • Peer Reviewed
• [Journal Article] 半正定値計画問題に対する行列補完理論の高速実装 (2014)
  • Author(s): 山下真
  • Journal Title: オペレーションズ・リサーチ Volume: 59(3)
• [Journal Article] The second-order reduced density matrix method and the two-dimensional Hubbard model (2013)
  • Author(s): James S. M. Anderson, Maho Nakata, Ryo Igarashi, Katsuki Fujisawa, Makoto Yamashita
  • Journal Title: Computational and Theoretical Chemistry Volume: 1003 Pages: 22-27
  • DOI: 10.1016/j.comptc.2012.08.018
  • Peer Reviewed
• [Journal Article] High-Performance General Solver for Extremely Large-scale Semidefinite Programming Problems (2012)
  • Author(s): Katsuki Fujisawa, Hitoshi Sato, Satoshi Matsuoka, Toshio Endo, Makoto Yamashita, Maho Nakata
  • Journal Title: International Conference for High Performance Computing, Networking, Storage and Analysis Volume: SC'12
  • Peer Reviewed
• [Presentation] Dual Approach Based on Spectral Projection Gradient Method for log-det SDP with ell_1 Norm (2014)
  • Author(s): Makoto Yamashita, Mituhiro Fukuda, Takashi Nakagaki
  • Organizer: SIAM Conference on Optimization
  • Place of Presentation: Town and Country Resort & Convention Center, San Diego, California (米国)
  • Year and Date: 2014-05-19
  • Invited
• [Presentation] An approach based on shortest path and connectivity consistency for sensor network localization problems (2012)
  • Author(s): Makoto Yamashita, I-Lin Wang
  • Organizer: International Symposium on Mathematical Programming 2012
  • Place of Presentation: TU Berlin
• [Presentation] High-performance Implementation of Positive Matrix Completion for SDPs
  • Author(s): Makoto Yamashita, Kazuhide Nakata
  • Organizer: INFORMS Annual Meeting 2013
  • Place of Presentation: Minneapolis Convention Center, (Minneapolis, USA)
  • Invited
• [Remarks] Download page for boxSDP-matlab
  • URL: http://www.is.titech.ac.jp/~makoto/software/boxSDP/
• [Remarks] SDPA Homepage
  • URL: http://sdpa.sourceforge.net